Moments of the Riemann zeta function

Abstract: For over a 100 years, $I_k(T)$, the $2k$-th moments of the Riemann zeta function on the critical line have been extensively studied. In 1918 Hardy-Littlewood established an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment $(k=2)$. Since then no other moments have been asymptotically evaluated. In the late 1990's Keating and Snaith gave a conjecture for the size of $I_k(T)$ based on a random matrix model. Recently I showed that an asymptotic formula for the sixth moment ($k=3$) follows from a conjectural formula for some ternary additive divisor sums. In this talk I will give an overview of these results.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca